$2\mathrm{.}5.$ A small motor is mounted on the end of a shelf in a submarine modeled as a beam with a tip mass ilustrated in Figure P$2\mathrm{.}5.$ The effect of the motor when running is to apply a force to the tip of the beam equal to $10cos[50t]lb.$ The weight of the motor is $10$ lb $.$ The shelf is $50$ in long, $20$ in wide, and $0\mathrm{.}5$ in thick. $($a$)$ Calculate the vibration magnitude of the shelf if it is made of steel